2026-09-21T00:23:42Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/85124 2023-07-11 col_2142_5131 col_2142_14800 com_2142_5130 com_2142_14799 com_2142_234

Prussing, John E. Jo, Jang-Won 2015-09-25T22:34:30Z 2015-09-25T22:34:30Z 10000-01-01 1997 1997 "A recent advance in sufficient conditions for a weak local minimum in optimal control problems is used to develop a procedure for applying second-order necessary and sufficient conditions for a minimum of a cost functional. For a system with n state variables, an improved Riccati equation solution method is used to transform a test for the unboundedness of a n x n matrix into a test for a scalar being zero. Application to one important second-order necessary and sufficient condition, the Jacobi no-conjugate-point condition, is introduced using the ""Shortest path between two points on a sphere"" problem. Second-order necessary and sufficient conditions are applied to various optimal control problems, including spacecraft trajectory problems with constant thrust acceleration and with time-varying low thrust acceleration for a power-limited rocket engine. A solution that simultaneously maximizes final orbit energy and minimizes propellant consumption is found that satisfies the usual first-order necessary conditions, but is non-optimal. Other example variational problems are investigated: Hamilton's Principle for several dynamic systems, including a circular orbit in an inverse-square gravitational field and projectile motion in a uniform field, as well as a simple example of Zermelo's problem. For those solutions that satisfy first-order necessary conditions but are non-optimal, a Genetic Algorithm is successfully used to find a global near-optimal solution of lower cost." Made available in DSpace on 2015-09-25T22:34:30Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 9737146.pdf: 4961942 bytes, checksum: 04e6cd9e329452d5a4a4fe58d81cc4cc (MD5) Previous issue date: 1997 Embargo set by: Seth Robbins for item 86405 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs U of I Only 157 p. Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997. http://hdl.handle.net/2142/85124 (MiAaPQ)AAI9737146 eng Operations Research Applications of Second-Order Necessary and Sufficient Conditions to Optimal Trajectories text Aerospace Engineering Aerospace Engineering University of Illinois at Urbana-Champaign Dissertation Ph.D.